- #1
courtrigrad
- 1,236
- 2
Hello all
Let us say we are given a sequence of order 2. By order 2 I mean that we have a sequence in which the differences between the terms forms a sequence of order 1, which has a constant difference between terms. How can I prove that the nth term of a sequence of order 2 can be represented as:
an^2 + bn + c?
Or more generally how would I prove that that the nth term of a sequence of order k can be represented as:
an^k + bn^k-1 +... + pn + q?
Any help would we greatly appreciated.
Thanks
Let us say we are given a sequence of order 2. By order 2 I mean that we have a sequence in which the differences between the terms forms a sequence of order 1, which has a constant difference between terms. How can I prove that the nth term of a sequence of order 2 can be represented as:
an^2 + bn + c?
Or more generally how would I prove that that the nth term of a sequence of order k can be represented as:
an^k + bn^k-1 +... + pn + q?
Any help would we greatly appreciated.
Thanks